The idea of the jam is to design a game based on someone's letter. They might ask for a puzzle game or an action game. The problem is that if you were to participate and use your TTRPG system, you already have decided a lot about the game before reading the letter. Mainly that it's going to be an RPG story. Your giftee might have no interested at all in playing RPGs.
So no, I don't think it's a good idea for you to join.
Thank you for asking first.